1. Field of the Invention
The present invention relates to a method of detecting and isolating fault in sensors and a method of accommodating fault in sensors using the same, and more particularly, to a method of detecting and isolating fault in sensors in a system including redundant sensors and a method of accommodating fault in redundant sensors using the same.
2. Description of the Related Art
Many systems such as control, navigation, and communication systems consist of various and complex subunits, and thus the hardware and software structure of those subunits are very complicated. Therefore, the importance of reliability of the whole systems has been increased.
The reliability of the whole systems can be enhanced by improving the reliability of respective subunits. In addition, the fault detection and isolation (FDI) can also ensure the reliability of the whole systems.
The terminology “fault” refers to an unexpected change occurring in a system, which degrades the performance of the whole system; the terminology “fault detection” refers to the indication that something is going wrong in the system; the terminology “fault isolation” refers to the determination of the exact location of the fault; the terminology “fault identification” refers to the determination of the magnitude and type or nature of the fault; and the terminology “fault accommodation” refers to the reconfiguration of the system using healthy components.
The fault can occur in any part of the whole system, and thus, the reliability of the whole system can be enhanced by securing the normal procedure of the whole system even when fault occurs in some of the whole system, which can be further described using the concept of “redundancy.” The redundancy refers to the duplicating of elements or means for performing required functions so as to secure the reliability of the whole system even when some of the elements or means are broken up. The redundancy is categorized into a physical redundancy (direct redundancy or hardware redundancy) and an analytical redundancy (functional redundancy). Thus, FDI are categorized into FDI using hardware redundancy and FDI using analytical redundancy.
For hardware redundancy, more sensors than required at the minimum are used. For example, two or more sensors are used to obtain a scalar variable, and four or more sensors are used to obtain a vector variable. Therefore, to obtain the hardware redundancy, redundant sensors are required and thus, the manufacturing costs are increased and the system is physically increased in size.
For analytical redundancy, additional information is obtained from the mathematical model of a system. This type of redundancy is based on the idea that inherent redundancy exists in a unique dynamic relationship between inputs and outputs of the system model. The FDI method using the analytical redundancy is complex on theory because there is a need to obtain the mathematical relationship between a plurality of sensors for measuring various physical values, and in most cases, redundant hardware is necessarily required.
For example, the inertial navigation system (INS), which is widely used in aerospace systems, uses redundant sensors for hardware redundancy. Although common INS uses three accelerometers and three gyroscopes to calculate navigation information such as position, velocity and altitude, redundant sensors are used to obtain reliability and to enhance navigation accuracy.
In a conventional FDI applied in the INS, fault is detected and isolated by comparing the information from redundant sensors, and specifically, the parity equation generation, fault detection, and fault isolation are sequentially performed. In addition, if possible, the system can be reconfigured using only the other sensors, excluding faulty sensors, which is a fault accommodation procedure.
The parity equation is obtained using either a vector of a null space of the measurement matrix to be independent from input values (angular velocity, acceleration velocity), or a residual. The obtained parity equation is compared with a predetermined threshold to detect and isolate fault. A lot of studies on FDI methods have been performed so far to produce parity equation through various methods, and a fault detection and isolation method is determined according to the structure of parity equation. Examples of a conventional FDI method include a look-up table method, a squared error method, a generalized likelihood ratio test (GLT), an optimal parity vector test (OPT), sequential FDI, and a singular value decomposition method.
Meanwhile, among parameters for determining the performance of FDI, critical parameters are fault detection probability, correct isolation probability, and wrong isolation probability. FIG. 1 illustrates parameters used to show the performance of a conventional FDI. As the probability of false alarm or the probability of miss detection is increased, the performed of FDI is degraded, in which the false alarm refers to the case that although there is no fault in fact in the system, fault detection is issued, and the miss detection refers to the case that although there is fault in fact, the fault is not detected. However, a high-performance FDI can be defined that even when fault occurs in the system and thus the fault is duly detected, only such sensors having the magnitude of fault greater than a predetermined level, that is, sensors outputting a fault signal of a predetermined threshold value (hereinafter, referred to as ‘exclusion threshold value’) or greater are isolated. Such selective isolation is required because more sensors should be used to improve a degree of accuracy of the whole system. That is, the high-performance FDI is required to have a high fault detection probability in a fault detection procedure, and a high correct isolation probability and a low wrong isolation probability in a fault isolation procedure.
However, a conventional FDI shows high performances when a relatively high fault signal occurs, but low performances when a relatively low fault signal occurs. This is because when a small exclusion threshold value is used to detect and isolate a fault signal, a false alarm probability and a wrong isolation probability increases. The conventional FDI determines an exclusion threshold value using only one parity equation to minimize the false alarm probability. In this case, however, the exclusion threshold value can be largely affected by measurement noises and thus as long as the measurement noises are not removed, the exclusion threshold value is inaccurate.
Also, the most of conventional FDI methods only focus on a single sensor fault. That is, a plurality of sensors faults, that is, double faults are not considered at all, or the double faults isolation performance on double faults is poor.